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Data Management Question help

In Bayfield, 65% of residents read the Bayfield Breeze, a local online blog. Dennis wants to know what people think of the blog, so he stops 40 people on the street to ask them if they read it.

1. Verify that the normal distribution can be used to approximate this situation.

2. What is the mean and standard deviation of the number of people he finds that read the Breeze?

3. What is the probability that at least 25 of the people he asks read the blog?

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Andy C. | Math/Physics TutorMath/Physics Tutor
4.9 4.9 (19 lesson ratings) (19)
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Sample size is N=40, so use Normal distribution
 
p=0.65 
Mean = n*p = 65% of 40 = 26
 
Std dev  =  sqrt ( 40 * 0.65 * 0.35 ) = 3.01662
 
Normal approximation to binomial
 
Prob ( X>-25) = 1 - Prob ( X < 25.5) <--- continuity correction
 
                      = 1 - Prob( z < (25.5-26)/3.01662)
                      = 1 - Prob ( z < -0.16575)
                      = 1 - 0.4345
                      = 56.55%